Journal
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 369, Issue 1956, Pages 4705-4729Publisher
ROYAL SOC
DOI: 10.1098/rsta.2011.0113
Keywords
uncertainty; dynamics; chaos; bifurcation
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The discovery of chaotic dynamics implies that deterministic systems may not be predictable in any meaningful sense. The best-known source of unpredictability is sensitivity to initial conditions (popularly known as the butterfly effect), in which small errors or disturbances grow exponentially. However, there are many other sources of uncertainty in nonlinear dynamics. We provide an informal overview of some of these, with an emphasis on the underlying geometry in phase space. The main topics are the butterfly effect, uncertainty in initial conditions in non-chaotic systems, such as coin tossing, heteroclinic connections leading to apparently random switching between states, topological complexity of basin boundaries, bifurcations (popularly known as tipping points) and collisions of chaotic attractors. We briefly discuss possible ways to detect, exploit or mitigate these effects. The paper is intended for non-specialists.
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